Spectrum

Hello, and welcome to today's physics lesson. In this session, we will explore the fascinating world of light and its many colours. Our chapter is titled Spectrum. We will learn how a simple glass prism can split white light into a rainbow of colours, discover the vast electromagnetic spectrum that extends far beyond what our eyes can see, and understand why the sky appears blue and the sun looks red at sunset. Let us begin this illuminating journey together.

When a ray of light passes through a triangular prism, it does not travel straight through. Instead, it bends or deviates from its original path. This happens because light changes speed when it moves from air into glass, and then again when it exits back into air.

Consider a light ray entering the first surface of a prism. It bends toward the base of the prism by an angle we call δ₁. Inside the prism, the light travels in a straight line until it hits the second surface. There, it bends again toward the base by another angle, δ₂. The total deviation, represented by the symbol δ, equals the sum of these two deviations. Verbally, delta equals delta one plus delta two. Symbolically, δ = δ₁ + δ₂. Here, δ is the total angle of deviation, δ₁ and δ₂ are the deviations at the first and second surfaces respectively. The unit of deviation is degrees.

This total deviation depends on three important factors. First, the angle at which light enters the prism, called the angle of incidence. Second, the angle of the prism itself, which is the angle between its two refracting surfaces. Third, and most crucially for our discussion, the refractive index of the prism material. Since refractive index varies with colour, different colours deviate by different amounts.

Here is a key insight about light and colour. All colours travel at the same speed in air, approximately three hundred million metres per second. But in glass or any other transparent medium, their speeds differ. Violet light, with its short wavelength of about 4000 Å or 400 nm, travels slowest in glass and is deviated the most. Remember, one nanometre equals ten angstroms, so one angstrom equals ten to the power of minus ten metres. Red light, with its longer wavelength of about 8000 Å or 800 nm, travels fastest in glass and is deviated the least.

Since refractive index increases as wavelength decreases, violet light experiences the greatest deviation, while red light experiences the least deviation. This wavelength-dependent behaviour is fundamental to understanding how prisms create spectra.

White light is not a single, pure form of light. It is a mixture of many colours, each with its own characteristic wavelength. The prominent colours in white light, arranged from shortest to longest wavelength, are violet, indigo, blue, green, yellow, orange, and red. You can remember this order using the acronym VIBGYOR.

Let me give you the approximate wavelength ranges for these colours. Violet spans 4000 Å to 4460 Å, or 400 nm to 446 nm. Indigo extends from 4460 Å to 4640 Å or 446 nm to 464 nm. Blue spans 4640 Å to 5000 Å or 464 nm to 500 nm. Green spans 5000 Å to 5780 Å or 500 nm to 578 nm. Yellow spans 5780 Å to 5920 Å or 578 nm to 592 nm. Orange spans 5920 Å to 6200 Å or 592 nm to 620 nm. And red spans 6200 Å to 8000 Å or 620 nm to 800 nm.

Notice that frequency follows the opposite pattern to wavelength. As wavelength increases across the spectrum, frequency decreases. This inverse relationship comes from the fundamental equation connecting them. Violet has the highest frequency at about 7.5 × 10¹⁴ Hz, while red has the lowest at about 3.75 × 10¹⁴ Hz.

One of the most beautiful experiments in physics was performed by Isaac Newton in the seventeenth century. Newton allowed a narrow beam of sunlight to enter a dark room through a small hole and pass through a glass prism. On a white screen placed beyond the prism, he observed a stunning band of colours, just like a rainbow. This band of colours is called a spectrum.

Newton's crucial conclusion was revolutionary. White light is not pure and simple. It is polychromatic, meaning it consists of many colours mixed together. The prism does not create these colours, it merely separates what was already present in the white light.

Let us define our terms precisely.

Dispersion is the phenomenon of splitting of white light by a prism into its constituent colours.

A spectrum is the band of colours seen on a screen when white light passes through a prism.

The cause of dispersion lies in how different wavelengths travel at different speeds in glass. When white light strikes the first surface of a prism, the colours begin to separate because each bends by a different amount. Violet bends most, red bends least. At the second surface, further refraction occurs, spreading the colours even more apart. Thus, the first surface produces the dispersion, while both surfaces contribute to the overall deviation.

Now, imagine you are looking at a glass prism and a parallel-sided glass slab side by side. Both cause refraction, but with very different results. In a prism, the two surfaces are inclined to each other, so the emergent rays of different colours travel in different directions, creating a clear, spread-out spectrum.

In a parallel-sided slab, however, the two surfaces are parallel. Although dispersion occurs at the first surface, the second surface bends each colour back so that all emergent rays become parallel to each other and to the original incident ray. The colours remain so close together that they appear to recombine into white light. This is why a glass window does not produce a rainbow effect like a prism does.

The visible spectrum we have discussed represents only a tiny fraction of all possible electromagnetic waves. Beyond the red end lie infrared radiation, microwaves, and radio waves, with progressively longer wavelengths. Beyond the violet end lie ultraviolet rays, X-rays, and gamma rays, with progressively shorter wavelengths. Together, these form the complete electromagnetic spectrum.

Arranged in order of increasing wavelength, the electromagnetic spectrum begins with gamma rays, then X-rays, ultraviolet rays, visible light, infrared radiation, microwaves, and finally radio waves. All these waves share remarkable properties.

First, they require no material medium for propagation, they travel through vacuum. Second, in vacuum, they all travel at the same speed of 3 × 10⁸ m/s. Third, they exhibit reflection and refraction. Fourth, they are not deflected by electric or magnetic fields. Fifth, they are transverse waves, meaning their oscillations are perpendicular to their direction of travel.

The relationship between speed, frequency, and wavelength is given by a fundamental equation. The speed of an electromagnetic wave equals its frequency multiplied by its wavelength. Verbally, the speed c equals frequency f multiplied by wavelength lambda. Symbolically, c = fλ. Here, c represents speed in m/s, f represents frequency in hertz, and λ represents wavelength in metres.

Let us briefly survey the properties and uses of different electromagnetic radiations.

Gamma rays have wavelengths shorter than 0.01 nm. They possess enormous penetrating power and can pass through thick metal sheets. They originate from radioactive substances and cosmic rays. Medically, they are used in radiotherapy to destroy cancer cells. Industrially, they check the quality of welds.

X-rays, discovered by Roentgen, have wavelengths from 0.01 nm to 10 nm. They are produced when highly energetic electrons strike a heavy metal target of high melting point. They penetrate flesh but are stopped by bones, making them invaluable for medical imaging and detecting fractures. They also reveal the atomic structure of crystals.

Ultraviolet radiation, discovered by Ritter, spans 10 nm to 400 nm. It is more chemically active than visible light, affects photographic plates, and causes fluorescence. It passes through quartz but is absorbed by ordinary glass. The sun emits ultraviolet radiation, but fortunately, Earth's ozone layer absorbs most of the harmful portion. Uses include sterilising medical equipment, detecting forged documents, and helping produce vitamin D in living organisms. However, excessive exposure causes skin cancer.

Infrared radiation, discovered by Herschel, ranges from 800 nm to 1 mm. Its most notable property is strong heating effect. It travels through rock salt but is absorbed by glass. Because of its long wavelength, it scatters less in atmosphere, penetrating fog and mist effectively. Applications include night photography, thermal imaging, remote controls, and therapeutic heating.

Microwaves, produced by electronic oscillators, range from 1 mm to 1 m in wavelength. They are essential for satellite communication, radar systems, and microwave ovens.

Radio waves, the longest electromagnetic waves, exceed 1 m in wavelength. They carry television and radio signals across vast distances.

Finally, let us understand why the sky appears blue and why sunsets are red. This phenomenon is called scattering of light.

When sunlight enters Earth's atmosphere, it encounters countless tiny molecules of gases and dust particles. These particles absorb light energy and re-emit it in various directions. This process is scattering.

The intensity of scattered light follows an important law. It is inversely proportional to the fourth power of wavelength.

Verbally, intensity I is proportional to one over wavelength lambda to the fourth power. Symbolically, I ∝ 1/λ⁴. Here, I is intensity of scattered light and λ is wavelength of incident light. This means shorter wavelengths scatter much more intensely than longer wavelengths.

This follows from the inverse fourth power law: since red light's wavelength is double that of violet, the scattering intensity ratio is two to the fourth power, or sixteen. However, our eyes are more sensitive to blue than to violet, so we perceive the scattered light as blue. This is why the sky appears blue when we look away from the sun.

At sunrise and sunset, sunlight must travel through much more atmosphere to reach our eyes. During this long journey, most of the blue and violet light gets scattered away in other directions. What remains is predominantly red and orange light, which scatters least and travels straight to our eyes.

This explains the beautiful red hues of dawn and dusk.

At noon, when the sun is overhead, sunlight travels the shortest path through atmosphere. All colours reach us with minimal scattering, so the sky appears white.

Clouds appear white because their water droplets and ice crystals are larger than the wavelength of visible light. Such large particles scatter all colours equally, mixing them back into white light.

Without an atmosphere, as on the moon, there would be no scattering. The sky would appear black, and stars would be visible even during daytime. Astronauts in space see exactly this: a black sky surrounding a brilliantly blue Earth, whose atmosphere scatters sunlight toward them. However, the sun and other heavenly bodies are seen without twinkling, since there is no atmospheric disturbance.

Red light is used for danger signals because its long wavelength scatters least. Even through fog or dust, red light travels farthest without weakening, making it visible from great distances. Similarly, infrared radiations are used in remote controls for televisions and other gadgets.

Let us recap the key takeaways from this lesson.

First, a prism deviates light toward its base, and the deviation depends on the wavelength, with violet deviating most and red least, following the order VIBGYOR.

Second, dispersion is the splitting of white light into its constituent colours, forming a spectrum. This occurs because different colours travel at different speeds in glass.

Third, the electromagnetic spectrum extends far beyond visible light, from gamma rays to radio waves, all sharing the same speed in vacuum and common wave properties.

Fourth, infrared and ultraviolet radiations lie just beyond the visible red and violet ends respectively, each with distinctive properties and practical applications.

Fifth, scattering of light by atmospheric particles follows the inverse fourth power law of wavelength, explaining the blue sky, red sunsets, and white clouds.

Sixth, the colour we perceive depends on which wavelengths reach our eyes directly versus which are scattered away.

Thank you for your attention throughout this lesson on the spectrum. I hope you now see the world of light with new understanding, from the rainbow created by a prism to the blue dome above your head. Physics reveals the hidden order in nature's beauty. Keep curious, keep questioning, and continue exploring the wonders of science. Until next time, goodbye and study well.